Find the reference number of 11pi/9

1 answer:

4 0

Unsure of what you mean by "reference number."

I do recognize that 11pi/9 is in quadrant III. I suspect that the so-called "reference number" is the acute angle between the end ray of 11pi/9 and pi, or, in more easily comparable numbers, between 9pi/9 and 11pi/9.

That difference is 2pi/9.

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3 years ago

In the diagram, is the perpendicular bisector of and is also the angle bisector of . If m = x, which quantity is equal to sin ?

earnstyle [38]

Given that line PN is a perpendcular bisector of line AB, then angles APN and BPN are equal to 90 degrees each.

Also, given that line PN is an angle bisector to angle CPD and angle CPD measures x, then the measure of angle DPN is $\frac{1}{2} x$ .

Thus, the measure of angle DPB = angle BPN - angle DPN
$=90- \frac{1}{2} x$

Therefore,
$\sin DPB=\sin\left(90- \frac{1}{2} x\right) \\ \\ =\sin(90)\cos\left(\frac{1}{2} x\right)-\sin\left(\frac{1}{2} x\right)\cos(90) \\ \\ =\cos(\frac{1}{2} x)$